If $\displaystyle x = \sqrt{2} + \frac{1}{\sqrt{2}}$ and $\displaystyle y = \sqrt{2} - \frac{1}{\sqrt{2}}$ then $\displaystyle x^2 + y^2$ is

$\displaystyle 3x-2:5x+6$ the duplicate ratio of $\displaystyle 2:3$ then find the value $\displaystyle x$.

The ratio of two numbers are $\displaystyle 3:4$. The difference of their squares is $\displaystyle 28$ greater is:

The price of scooter and moped are in the ratio $\displaystyle 7:9$. The price of moped is $\displaystyle ₹1,600$ more than that of scooter. Then the price of moped is:

If $\displaystyle A:B=3:7$, then $\displaystyle 3a+2b:4a+5b=?$

The ratio of number of boys and the number of girls in a school is found to be $\displaystyle 15:32$. How many boys and equal number of girls should be added to bring the ratio to $\displaystyle 1:2$?

In a certain business A and B received profit in certain ratio B and C received profits in the same ratio. If A gets $\displaystyle ₹1600$ and C gets $\displaystyle ₹2500$ then how much does B get?